Archive for February, 2012

Previously we have discussed about math help solver and In today’s session we are going to discuss about Linear Equations, They are expressed as the combination of terms and operators placed on the left and right side of the equation . In Algebra, the equations are to be solved by different methods like elimination method, substitution methods and Two Step Linear Equation solution method.

As the name suggests, a Two Step Linear Equation method of solving the algebraic equation involves two steps to get the solution to the unknown variable. Let us learn it more clearly through this example. Let the given equation be

4y + 3 = 19

Here we need to find the value of unknown variable Y. In first step, We first subtract 3 from both the sides and get:

4Y + 3 – 3 = 19 – 3

Or

4Y = 16

Now to get the value of Y , we divide both sides of the equation by 4, This is the second step towards the solution.

We get:

4Y/4 = 16/4

or Y = 4 Ans

In the above equation, we observe that in the first step the addition operator is removed by introducing the operation of subtraction and in second step, the operation of multiplication is eliminated by simply dividing the equation by 4. So we get the result of Y in two steps. Such solutions to the complex linear equations is called Two Step Linear Equation.(Know more about Linear Equation in broad manner, here,)

Linear equations play a vital role in solving the problems of the real life and to get the output of the variables introduced to the equations. We need to decide, which operator has to be performed. Just remember that if addition is to be eliminated, we need to introduce subtraction and vica- versa. Similarly if multiplication is to be removed, we need to divide and vice- versa.

Hello students, Previously we have discussed about irrational numbers examples and in this session we are going to know about Finding Solution Of Simultaneous Equations By Graphing. The method or procedure of solving a system of simultaneous linear equation of two variables by drawing their graphs is known as the graphical method. We know that the graphical representation of a linear equation in two variables is a straight line such that every point on the line represents a solution of the equation and every solution of the equation is represented by a point on the line.

Thus if there is a system of simultaneous linear equation in two variables such that the line representing the equation intersect at a point P ( a, b ). clearly the point P lies on both the lines, so its coordinates will satisfy the both the equation in the system. Thus x = a, y = b is the solution of the given system of equation.(Know more about Simultaneous Equations in broad manner, here,)

We may use the following algorithm for the Solution of Simultaneous Equations by Graphing for two variables :-

Algorithm :-

Step 1:- Obtain the given system of simultaneous linear equation in x and y.

let the system of simultaneous linear equation be

a1x + b1y = c1…………….1

a2x + b2y = c2…………….2

Step 2 :- draw the graph of the equation 1 and 2 in step 1.

then lines L1 and L2 will represents the graphs.

Step 3 :- If the lines L1 and L2intersect at a point and ( a, b ) are the coordinates of this points, then the given system has a unique solution given by x = a, y = b, otherwise go to step 4.

Step 4 :- If the lines L1 and L2are coincident, then the system is consistent and has infinitely many solution. In this case, every solution of one of the equation is a solution of the system, otherwise go to step 5.

Step 5 :- If the lines L1 and L2are parallel, then the given system of equation is in- consistent that is it has no solution.

Previously we have discussed about how to find the area of a hexagon and In today’s session we are going to discuss about Unique solution Linear Algebra, It is studied in context of solving the equations of Linear Algebra. To find the solution of a pair of equations, draw it on the graph and if they meet at only one point then such solution of equation is called the unique solution of the linear equation.

Linear Equation is the equation in which we have equations in two variables. To solve these equations we have various methods.

First method to solve the equation of Linear Algebra is the method of substitution.

Unique solution Linear Algebra is the set of two linear equations which have only one common point . These two equations intersect at only point when we draw such lines on the graph.

Let us assume any system of linear equations say

ax + by + c = 0 and dx + ey + g = 0

This set of equations from will have a unique solution if the two lines which are represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at only one point. Through this we directly come to the conclusion that these set of lines are not parallel.

Also if they are not a pair of parallel lines, the two lines should have different slopes.
We also conclude from this:
ax + by + c = 0 and dx + ey + g = 0 will not represent two parallel lines if their slopes are different.

I.e. when the ratio of coefficient of x and y are not equal. It implies:

Hello students. Previously we have discussed about free online tutoring for math and In this subdivision, we are going to learn about the linear equations and their graphs on the co-ordinate plane. We will find out how to deal with linear equations graphs in the algebra.Graphing linear equations is a pretty simple work. It merely entails some of the computations regarding the variables present in the equation and then plotting them on the co-ordinate axis.
Before going through the graphing linear equations we have to understand the concept of linear equations. The linear equations are the type of the equations which are represented in the form of equation of one or two variables. The equation of two variables x and Y can be given as Y = ax + b, where ‘a’ and ‘b’ are two numbers. The constant term ‘b’ is the intercept in the equation with the Y co-ordinate axis. All such linear equations always form linear graphs or we can say they form a line.
Now proceeding with an example, let we have a equation of a line f (x) = y = x + 2. Now for the intermediate points of the graph we have to solve this linear equation with the help of putting values in the equation. We first finds all the related and corresponding values of both ‘x’ and ‘y’. Just like the below calculation we uses the table for the values and calculates the corresponding values. Here we have values:
Value of X: -2 0 1 2 3 4
Values of Y: 0 2 3 4 5 6
Using all these values we can make a graph for the linear equation y = x + 2. Now plotting these values on the co-ordinate plane we will get the resultant graph for the equation:

Previously we have discussed about differential calculus and In today’s session we are going to discuss about Graphing Linear Equations with One Variable, Graph designing is interesting and easier part of the discrete mathematics. In the discrete mathematics we study about the diagrammatic representation of the graph. Graph is an illustrative representation of points, which are directly or indirectly interconnected to each other. In the graphical representation we are analyzing the various paths, calculation and size of the program. Points are shown by vertices of the graph and interconnecting lines shown by edges of the graph. Through this blog we are going to discuss about Graphing Linear Equations with One Variable.

Linear Equations are the equations, which are collection of variable and numbers. In linear equation we find out the value of the variable which satisfies the given equation.

To create graph of linear equation we have to follow some steps:

1) Select the value of x and find the value of y.

2) Prepare the table of values of x and y

3) Then plot those values on graph by taking appropriate scale.

4) After plotting the points arrange them by a creating straight line.

Example: Draw the graph y = 2x

Solution: Here we take the Linear Equations with One Variable, where values of y depend on the values of x.

Value of x

1

1.5

2

2.5

Value of y

2

3

4

5

When we put the value of x in the given equation then we obtain the value y, which is given in the table. Now we put these values in the graph. In the below given graph we show you how to plot the equations value in the graph.

This is the graph of y = 2x. Similarly we can draw graphs of other linear equations.

Hello students, Previously we have discussed about slope worksheet and today I am going to discuss about Linear Equation in Two Variables. A equation of the form ax + by + c = 0 where a, b, c are real numbers is called a linear equation in two variables x and y.

Let us see some Linear Equation in Two Variables examples.

Example :- show that x=3 and y= 2 in the equation of 5x – 3y = 9

Solution:-

step1:- put x=3 and y=2 in the given equation, we get

step 2:- L.H.S =5*3-3*2 = 9(R.H.S)

step 3:- 15 – 6 = 9(R.H.S)

step 4:-so, x=3 and y=2 is a solution of 5x-3y=9

step 5:- L.H.S=R.H.S

Now, we will discuss about simultaneous linear equations in two variables.

Two linear equation in unknown variables x and y are said to form a system of simultaneous linear equations if each of them gets satisfied by the same pair of values of x and y.

Example:- show that x=5, y=2 is a solution of the system of linear equations.2x + 3y = 16, x – 2y = 1

Solution:-

step 1:- the given equations are:-

2x +3y =16

x-2y =1

step 2:- putting x =5, y =2 in eq.(1) we get:

L.H.S= (2*5+3*2)=16=(R.H.S)

Step 3:-putting x =5, y =2 in eq.(2) we get:

L.H.S= (5-2*2)=1=(R.H.S)

so, x=5, y=2 satisfy both eq(1) and eq(2). It is a solution of the given system of equations.

Now, we will talk about consistent and inconsistent systems of linear equations in two variables.

First one is consistent system of linear equation . A system of two linear equations in two unknown variables is said to be consistent if it has at least one solution.

Second one is inconsistent system of linear equation. A system of two linear equations in two unknown is said to be inconsistent if it has no solution at all.

Hello friends,Previously we have discussed about math problem solver with steps for free and in this blog we are going to discuss about Addition Method of Linear Equations. We know that a linear equation is an equation that is represented in the form ax+by+c =0, where a, b, c are real numbers.

Linear equations can have two and more variables. Let us take some examples of Adding Linear equations to.

Example 1 :- solve the following equations by addition linear method

4 a + b = 15

3 a – b = 10

solution :-

step 1 :- the given system of equation is written as follows

4 a + b = 15

3 a – b = 13

………………………..

=> 7 a = 28 ( adding both equations as b variable in the equations has the opposite signs and so it will be cancel out )

step 2 :- now, we can calculate the value of a variable and get the value of a that is 7 a = 28

a = 28 / 7 = 4

putting the a = 4 in equation (1) we have

step 3:- 4 (4) +b = 15

step 4:- 16 + b =15

step 5:- b = 15 – 16

step 6 :- b = -1

Then the solution is ( a, b ) = ( 4, -1 )

Now, to check if this answer is correct, put the value of a as equal to 4 in equation (2) we have